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3 years ago

(b). Solve for x and verify the result: 5x + 3 = 4/3 (1+x)

Mathematics

2 answers:

Kazeer [188]3 years ago

6 0

<h2><u>Solution :</u></h2>

${\dashrightarrow\sf{5x + 3 = \dfrac{4}{3} \bigg(1 + x \bigg)}}$

${\dashrightarrow\sf{3 \bigg(5x + 3 \bigg)= 4\bigg(1 + x \bigg)}}$

${\dashrightarrow\sf{\bigg(5x \times 3 + 3 \times 3 \bigg)= \bigg(1 \times 4 + x \times 4 \bigg)}}$

${\dashrightarrow\sf{\bigg(15x + 9 \bigg)= \bigg(4 + 4x\bigg)}}$

${\dashrightarrow\sf{15x - 4x =4 - 9 }}$

${\dashrightarrow\sf{11x =4 - 9 }}$

${\dashrightarrow\sf{11x = - 5 }}$

${\dashrightarrow\sf{x = - \dfrac{5}{11}}}$

$\bigstar{\underline{\boxed{\sf{\red{x = - \dfrac{5}{11}}}}}}$

<u>∴ The value of x is -5/11.</u>

$\begin{gathered}\end{gathered}$

<h3><u>Verification :</u></h3>

${\dashrightarrow\sf{5x + 3 = \dfrac{4}{3} \bigg(1 + x \bigg)}}$

${\dashrightarrow\sf{ \bigg(\left\{5 \times - \dfrac{5}{11} \right\} + 3 \bigg)= \dfrac{4}{3} \bigg(1 + \left\{ - \dfrac{5}{10}\right\}\bigg)}}$

${\dashrightarrow\sf{ \bigg(\left\{- \dfrac{25}{11} \right\} + 3 \bigg)= \dfrac{4}{3} \bigg(1 + \left\{ - \dfrac{5}{11}\right\}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{ - ( 25 )+ (3 \times 11)}{11} \bigg)= \dfrac{4}{3} \bigg( \dfrac{(1 \times 11) - (5 \times 1)}{11}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{ - 25+ 33}{11} \bigg)= \dfrac{4}{3} \bigg( \dfrac{11 - 5}{11}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \dfrac{4}{3} \bigg( \dfrac{6}{11}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg(\dfrac{4}{3} \times \dfrac{6}{11}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg(\dfrac{4 \times 6}{3 \times 11}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg(\dfrac{24}{33}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg(\cancel{\dfrac{24}{33}}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg({\dfrac{8}{11}}\bigg)}}$

$\bigstar{\underline{\boxed{\sf{\red{LHS = RHS}}}}}$

<u>∴ Hence Verified !</u>

Nata [24]3 years ago

3 0

Answer:

$x = - \frac{5}{11} \\$

Step-by-step explanation:

$5x + 3 = \frac{4}{3} (1 + x) \\ 5x + 3 = \frac{4}{3} + \frac{4x}{3} \\ 5x - \frac{4x}{3} = \frac{4}{3} - 3 \\ \frac{3(5x) - 4x}{3} = \frac{4 - 3(3)}{3} \\ \frac{15x - 4x}{3} = \frac{4 - 9}{3} \\ \frac{11x}{3} = - \frac{5}{3} \\ 11x = - \frac{5}{3} \times 3 \\ 11x = - 5 \\ x = - \frac{5}{11} \\$

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Please help! 20 points and crown!

maw [93]

The answer is: [C]: " 0.5 " .
________________________________________
Explanation:
________________________________________
Let us examine all the inputs ("x-values") listed that are "one unit apart"; and see what the corresponding "outputs" (that is: the "f(x)" values) are—and how far apart the corresponding "outputs" are.
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Refer to the table (provided within the actual question):;
_____________________________________________________
→ And start with the beginning values for the "inputs" (or; "x-values") listed; which are in "chronological order", from: "x = -3" to "x = 3" ; and all the "x-values" provided are "1 (one) unit apart" ; and: "inn chronological order, from least ("x = -3") to greatest ("x = 3")" .
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When: x = -3 ; f(x) = -0.5 ;

When: x = -2 ; f(x) = 0 .
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The inputs, "-3" and "-2" , are ONE (1) unit apart.

→ Note: | [-3 − (-2)] | = | (-3+2) | = | (-1) | = " 1 " (one) unit apart.

The corresponding "outputs" are "0.5 units apart" .

Note: | (-0.5 − 0) | = | (-0.5) | = 0.5 ; → "0.5 units apart" .
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Then continue, in chronological order, with the values listed on the table (provided within the actual question):
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→ Note: | [-2 − (-1)] | = | (-2 + 1) | = | (-1) | = " 1 " (one) unit apart.

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(b). Solve for x and verify the result: 5x + 3 = 4/3 (1+x)​

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